You have a job in a University research group investigating the effect of solar

Question

You have a job in a University research group investigating the effect of solar flares on
the Earths magnetosphere. Your team is designing a small, cheap satellite for the
investigation. As soon as the satellite achieves a stable orbit, it must extend its two solar
panels. Your team must design a lightweight power source for deploying the solar
panels. You have been asked to investigate the use of capacitors as a power source.
You decide to calculate how the mechanical energy transferred to a device powered by
a capacitor depends on the capacitance. You will test your calculation using a
laboratory model in which a capacitor provides power to a motor that lifts a mass. You
calculate how far the weight will move as a function of the capacitance of the capacitor.
You assume that you know the initial voltage on the capacitor.

1. Draw pictures of the situation before the weight moves, while the weight is in
motion, and after the weight has come to rest. Label all relevant distances, masses,
forces, and potential differences. Describe the physics principles you need to solve
this problem.
2. Define the initial and final times of interest in this problem. Describe (perhaps with
your diagrams) what happens to energy in the situation between those times.
3. Are there objects in the problem whose potential or kinetic energy is relevant, and
that you can calculate directly in terms of quantities measurable in the lab? If so,
write down expressions for their initial and final (potential or kinetic) energies.
4. Use the work-energy theorem to write an equation for the net work done on the
weight. Use this equation and equations from previous steps to write the amount of
energy transferred from the capacitor to the weight, during the entire process, as a
function of the distance the weight moves.
5. How would you define efficiency for this situation? Choose a system. Write an
energy conservation equation for your system that relates the efficiency, the
situations initial conditions, and properties you can measure in the lab, to the
distance the weight moves.
6. Use the principal of energy conservation to write an equation for the amount of
energy dissipated in this situation, in terms of measurable quantities and the
efficiency. Be sure this equation is consistent with your description from step 2.
7. Sketch a graph of the distance the weight moves as a function of the capacitors
capacitance. Assume constant efficiency, and that the capacitor is charged to the
same potential difference for each trial. (You can check the constant efficiency
assumption in the lab.)

Explanation / Answer

1. Energy transformations--------------->>> The idea that a capacitor is a store of electrical energy may have already emerged in previous sections but it can be made clear by using the energy stored in a capacitor to lift a weight attached to a small motor. The energy transfer process is not very efficient but it should be possible to show that a larger pd (or a higher capacitance) lifts the weight further. Hence energy stored depends on both C and V. :::::::: 2. Calculating energy stored-------->>> Having seen that the energy depends on the voltage, there are several approaches which lead to the relationship for the energy stored. Start with a reminder of the idea that

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